Sunday, November 13, 2011

The Problem of Common Sense - Another Preview to IDHEF

I've been reading further into IDHEF and have been noticing they are asking the readers a number of questions, primarily "What would you do?" questions. I assume the point is to appeal to the reader's common sense. By definition, there is a huge problem with common sense. The Free Dictionary defines it as follows:

Sound judgment not based on specialized knowledge; native good judgment.

Using common sense is fine when people are dealing with things that don't require specialized knowledge, but, all too often, people try to apply common sense to things that are beyond, well, "common" knowledge.

I have observed this quite regularly recently with conservative politics in regards to economic policy. When it comes to debt control, for example, there have been many politicians comparing government budget management to the way people manage their personal budgets. The idea is that people have developed a "common sense" toward budget management and this can be applied to the government. The problem, though, is that government has different goals and serves a different purpose than an individual, not to mention that it operates on a much larger economic scale (macroeconomics for the government vs. microeconomics for an individual). UPDATE: I have learned that this flawed thinking is known as a false analogy. Yet, it would seem that the flaw is a result of using simple "common sense" thinking.

Another favorite case of mine is the Monty Hall problem. Just watch the video for starters.

As the guy said, most people, including myself, initially think it is 50/50. And, if you read the comments, you will likely find people who still think it is 50/50 after the solution is explained. The confusion comes from people appealing to their "common sense." If a person entered the problem with just the choice of two doors, it would be 50/50. Common sense recognizes this, but fails to recognize that the initial choice in a door and the revealing of a goat adds information to the puzzle. Ultimately, common sense ends up being wrong.

Getting back to IDHEF, I have been seeing, as previously stated, questions where the goal seems to be to get the reader to use their common sense. I think common sense ends up being wrong in many of these instances. I won't go into any particular examples here, but I want readers of the book to be wary of this and to think questions through thoroughly. It also wouldn't hurt to apply this in real life as well.

A bat and a ball together cost $1.10. The bat costs a dollar more than the ball. How much does the ball cost?

Apparently a lot of people will answer $0.10. What they seem to do is just subtract that $1 from the total. But if the ball costs $1.10, then the bat has to cost $1.10, bringing the total to $1.20. Yet, the total was given as $1.10. A little extra thought has to be put into this to figure out that the ball actually costs $0.05 (and thus the bat costs $1.05).

The webpage I found that had that example also has a nice probability question that makes for a good example:

Now, think about tossing a coin six times. Which is more likely: heads-heads-heads-tails-tails-tails or tails-tails-heads-heads-tails-heads?

You might think that the second one seems more random, so it's more likely. That error would fall into what Kahneman and Tversky would call the representativeness heuristic or, more specifically, the misconception of chance -- in other words, we tend to go on our intuitive notions of what an unrigged coin toss should look like rather than actually calculating.

If you think about the probabilities of each, you'll realize the two combinations are equally likely.

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